1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Resistance equivalent to a circuit

  1. Sep 29, 2009 #1

    Suppose I have the following circuit (excuse the ugly drawing):

    Suppose the generator is 1A and all the resistance are 1 Ohm (the values are not important). Moreover, suppose I already have all the voltages in V1, V2, V3, V4 (which I got using nodal analysis), and V0 is set to ground (V0 = 0).

    How do I get the total resistance from point A to point B (or node V0)? Can I use the results I got from nodal analysis for this?

    Please note my knowledge of electrical circuits is very basic, as this is not my field. I am using this to build an artificial Hex player, and resistance provides a good connectivity measure from each side of the board (see page 2 in http://home.earthlink.net/~vanshel/VAnshelevich-01.pdf).
  2. jcsd
  3. Sep 29, 2009 #2

    The Electrician

    User Avatar
    Gold Member

    The voltages of V1 and V2 must be the same since they are connected by a wire.

    The voltages of V3 and V4 must be zero since they are connected together by a wire which is also connected to ground.

    For this circuit, since you are exciting it with a current source of 1 amp, then the resistance from A to B (ground) is equal to the voltages at V1 and V2, which are the same.
  4. Sep 30, 2009 #3


    User Avatar
    Science Advisor

    Any resistors you have shorted out can be replaced by wires.

    That only leaves 3 resistors in parallel in the middle of the diagram.

    They are all 1 ohm, so ....... what is the total resistance?
  5. Sep 30, 2009 #4
    Are you saying that the resistance from A to B is R = V1/I = V1 Ohm = V2 Ohm?

    Also, why is the voltage the same in V1 and V2, if current can flow from A to V1 and V2? Shouldn't V1 and V2 have a lower potential than A?

    @vk6kro: I wanted to avoid that kind of analysis, since this circuit is not "fixed". Its just the simplest case of a much larger circuit that may look different (resistances with value=+infinite or 0), and I want a way to solve this that is easy to code into a program that does it (an algorithm, so to speak).

  6. Sep 30, 2009 #5

    The Electrician

    User Avatar
    Gold Member


    The voltage is the same at V1 and V2 because they are connected together by a wire.

    In schematics such as you have shown, a simple line represents a wire, which is assumed to have zero resistance.

    Real wires don't have zero resistance. They have some finite, non-zero resistance, but if you want to treat that in a circuit you would usually insert a resistor symbol of some low value like 500 microhms to represent the wire resistance. In the absence of any such representation of the non-zero resistance of a wire, the wire is treated as though it has zero resistance.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook